1. Field of Invention
The invention concerns a method for the determination of local similarity of geological units in the subsurface from a seismic 3-D dataset, which consists of a multitude of traces, each of which being formed by a sequence of data points that carry amplitude values, or seismic attributes derived therefrom.
2. Related Art of the Invention
Seismic reconnaissance methods are used worldwide in order to obtain additional knowledge on the distribution of geological structures in the subsurface, in addition to the information from drilled wells. The information from seismic data often allows to renounce on further reconnaissance wells, or to reduce their number to a minimum.
For the seismic reconnaissance of the subsurface, sensors (geophones/hydrophones) are used. Being aligned in a line (2-D seismics), they receive sound waves. These waves are emitted by a seismic source, e.g. by an explosive charge, vibrators, or airguns, and they are partially reflected back to the surface by subsurface layers. There they are registered, and recorded in form of a time series. This time series represents the arriving seismic energy in form of amplitude fluctuations. It is stored digitally, and consists of regularly spaced data samples, which are characterized by the respective time and by the corresponding amplitude value. Such a time series is called a seismic trace. The recording line moves across the area to be examined, and thus this a 2D seismic profile is recorded with this geometry.
The subsequent processing aims at a noise suppression, e.g. by stacking, or by dedicated application of filters. After stacking, which sums up those reflection amplitudes that are assigned to the same subsurface points, the term ‘poststack data’ is used. The results are vertical profiles, with a time or depth dependent representation of amplitudes and traveltimes, as well as attributes derived from the amplitudes, which serve as a basis for further geologic evaluation. The geologic layers can be followed on a profile by the lateral alignment of amplitudes.
If data are not recorded along a line but in an areal grid, a three-dimensional data volume results. In the case of a 3-D volume, an amplitude values is assigned to an arbitrary point in the subsurface, which may for example be described by Cartesian coordinates. The vertical direction is measured in time (traveltime of sound).
In this case, a large amount of data is produced (several Gigabytes), which are stored and subjected to the processing, before the actual interpretation e.g. for the further reconnaissance of the subsurface is possible. These processes require large computer resources and software, in order to process and correct the recorded signal. The result is given by poststack data, that represent a seismic volume in form of a 3-D dataset. The 3-D dataset represents physical and structural characteristics of the subsurface in a seismic image.
From this dataset, arbitrary cuts may be extracted, e.g. vertical profiles, and horizontal maps from different depths, which are interpreted in the following by geophysicists and geologists. Since this interpretation of the achieved seismic images mainly comprises an optic correlation, attempts have been performed to automatize this subjective evaluation that depends on one, or more interpreters.
Accordingly, the U.S. Pat. Nos. 5,563,949 and 6,092,026 describe a method, which highlights faults and zone of low coherency in a three-dimensional volume of stacked seismic data. This data volume is subdivided into a number of horizontal slices, and these slices are again subdivided into a number of cells. The cells contain portions of at least three seismic trace each, in a horizontal configuration that allows a comparison in two pre-defined vertical planes, e.g. along the inline and crossline directions. As mathematical methods for determining the similarity, or coherency of the traces in these planes, the cross-correlation and the covariance are explicitly mentioned. The maxima of the cross-correlations allow an estimation of the partial dip in the respective planes. These maxima can be determined for both correlation planes, and be combined into a single coherency value by a mathematical Operation. To each processed cell, the corresponding coherency value is assigned, and a new seismic volume of the coherency derived in this way, is thus created.
The calculation of trace similarity and dip by comparison of two traces in inline direction, and in crossline direction, respectively, is very sensitive to noise. Large time windows have to be chosen in order to obtain stable results, thus reducing the resolution. The method measures the local similarity/dissimilarity in cells, that possess a fixed form and orientation with respect to the coordinates of the seismic data volume. A continuous, distance dependent correlation, and possibly as well direction dependent correlation of the data can not be considered. The seismic data contained in the cell is entered into the measurement of local similarity/dissimilarity with a constant weight.
A further method is known from the U.S. Pat. No. 6,141,622, which measures the local similarity, or dissimilarity, respectively, of the seismic data in a three-dimensional seismic data volume. The measurement is carried out in a cell with vertical extension in time, and horizontal extension in the inline-crossline plane.
The traces used for the measurement are located either on one line, i.e., on an inline or crossline, or they are located on two lines, i.e., on an inline and on a crossline, symmetrically to the intersection of both lines. On these lines, 3, 5, or 7 neighboring traces are selected. The semblance, or the inverted semblance is measured in the cells. The measurement is performed exclusively along the inline, or crossline included. For the two directions contained the x-shaped cell, two measurements are obtained, that are then summed together.
The method measures the local similarity/dissimilarity in cells, that possess a fixed form and orientation with respect to the coordinates of the seismic data volume. A continuous, distance dependent correlation, and possibly as well direction dependent correlation of the data can not be considered. The seismic data contained in the cell is entered into the measurement of local similarity/dissimilarity with a constant weight. Dip is not considered.
The U.S. Pat. No. 6,138,075 describes a method that measures the local similarity, or dissimilarity of seismic traces in a three-dimensional seismic data volume. For the measurement, a cell is defined in the vertical direction along the traces, and in the horizontal plane. The cell contains a reference trace, and at least two neighbor traces. For each neighbor trace, an individual value of the similarity to the reference trace is determined by applying mathematical measures like semblance, or cross-correlation. The local dips of the data volume are taken into account by vertically shifting the neighbor traces in a pre-defined range, and selecting the maximum similarity value. The neighbor trace with the largest similarity value is declared the target trace. Then all similarity values that have been derived up to this stage, are regarded as preliminary, and are deleted. The final similarity measurement takes place exclusively between
The reference trace and the target trace, and it may well use a different similarity measure, e.g. the ‘Manhattan distance’.
The determination of similarity values by comparison of two traces, respectively, is very sensitive to noise. The limitation of the comparison to neighbor traces is not suited to detect gradual changes of the seismic behavior, which extend over distances of the order of many trace intervals, and where the change in the range of one trace interval is below the noise level of the data.
Another method is known from the U.S. Pat. No. 6,151,555, or WO 00/54207, respectively, which measures the local dissimilarity of seismic traces in a three-dimensional data volume. Tow alternative measures of the dissimilarity are given, following the concept of the statistical variance. For the measurement, a cell is defined in the vertical direction along the traces, and in the horizontal plane. For the horizontal plane. quadratic cells with 3×3 or 5×5 traces, as well as an x-shaped cell with 5+5 traces in both orthogonal directions, are offered for selection. The vertical extension of the cell is described by the number of contained samples along each single trace; this simultaneously represents the number of horizontal data slices. A triangular weight function assigns a weight to each horizontal data slice. Within the horizontal plane, however, no weighting takes place. Hence, each horizontal position contributes in the same way to the measure of dissimilarity. In each horizontal data slice, the mean, the sum of the squared deviations from the mean, and the sum of the squares is derived from data values contained in the slice. Two measures of dissimilarity can be calculated from these quantities as follows:    1. The sums of the squared deviations are multiplied with the vertical weight function, and summed for all horizontal data slices; the sums of the squares are treated equivalently, and finally the former are divided by the latter.    2. Alternatively, an individual quotient is calculated for each horizontal data slice, by dividing the sum of the squared deviations by the sum of the squares; these quotients are multiplied with the vertical weight function, and finally summed for all horizontal data slices.
The method measures the local dissimilarity in cells, which possess a fixed form and orientation with respect to the coordinates of the seismic data volume. A continuous, distance dependent correlation, and possibly as well direction dependent correlation of the data can not be considered. The seismic data contained in the cell is entered into the measurement of local similarity/dissimilarity with a constant weight. A consideration of dip does not take place.
Furthermore, a method is known from the DE 199 33 717 C1 which relates to the similarity analysis of data points belonging to a pre-defined three-dimensional environment of the analysis point just considered in a three-dimensional seismic dataset. The three-dimensional seismic dataset consists of a multitude of traces, each of which is composed as a sequence of data points to which amplitude values are assigned, or seismic attributes derived from amplitude values. This method, however, calculates the similarity of local sections of seismic data from the measurement dataset to a reference section corresponding to a pre-defined location and depth, and assigns this similarity value as an attribute to the central value of the corresponding local section.
A method is known from the WO 97/13166, which measure the local dissimilarity of seismic traces in a three-dimensional seismic data volume with a semblance method. For the measurement, a cell is defined in the vertical direction along the traces, and in the horizontal plane. In the horizontal plane, the cell has an elliptical, or rectangular shape, and it is centered at the analysis point. The main axis of the cell may exhibit an arbitrary angle to the horizontal co-ordinate axis of the seismic data. However, its orientation with respect to the data grid is then rigidly fixed by this angle. The measurement of the similarity may thus include one direction of preference at most, which is defined by the direction of the main axis. The vertical extension of the cell is described by the number of contained samples along each single trace; this simultaneously represents the number of horizontal data slices.
The semblance is calculated with in the cell for complex traces, i.e., for each real trace, a Hilbert transformed imaginary trace has to be derived. An estimation of the coherency follows from the averaging of the semblance over the vertical extension of the cell. In each horizontal data slice, the sum of the real values, and the sum of the Hilbert transformed values are calculated. Each of these sums is subsequently squared. These squared amplitude sums of all horizontal data slices are summed in order to form the numerator of the semblance. The denominator contains the sum of the squares of all real, and Hilbert transformed single values that are contained in the cell. The semblance in calculated as a dip dependent quantity, with dip being described by two parameters. These parameters are the apparent dips in the directions of the orthogonal horizontal data axes. They can be transformed into the parameter pair of dip and azimuth angles. For the dip dependent semblance calculation, the vertical position of the cell in the three-dimensional data volume is changed, whereas its horizontal shape and centering at the analysis point is preserved. The cell is sheared according to the apparent dips, i.e., the partial sums for the semblance calculation are derived in correspondingly dipping data slices. The dips to be considered are limited by a maximum dip angle. Three alternative schemes for the discretization of the solid angle are given in a polar representation of the dip and azimuth angle. The discretization may be performed with a quadratic, a triangular, or a radial grid. The radial grid is hereof regarded as disadvantageous.
Contrasting to the other schemes, it involves a highly non-uniform discretization of the solid angle.
The presented method does not use weighting in the horizontal plane, which could take into account a decrease of the lithologic and structural correlation of geologic bodies with distance. A temporal weighting is not applied either. The horizontal cell may possess a direction of preference, the orientation of which remains unchanged during the whole process of the similarity or coherency determination in the three-dimensional data volume. Hence, during the dip measurement, this rigidly oriented cell is not oriented according to the dip azimuth, i.e. to the direction of structural strike that varies more or less in the considered volume. If the directions of geologic strike, which are assumed during the dip dependent similarity measurements, vary with respect to the direction of preference of the cell, this may be disadvantageous, since the direction of largest continuity in geological bodies often has a relation to the direction of geological strike. Consequently, a possibly existing direction of preference of the cell may be oriented partly in parallel, partly perpendicular, and frequently with other angles to the directions of geologic strike of the considered dips. However, here it is possible that the measured similarity values render a distorted view of the exising dip dependence in the data, since the measurement renders systematically increased, or decreased similarity for some azimuth ranges due to the orientation of the analysis cell.
Moreover it is disadvantageous, that the Hilbert transformed imaginary trace must be calculated for each real trace within the calculation of similarity with consideration of dip and dip azimuth. This additionally requires significant calculation capacities. This method known from the WO 97/13166 is also revealed with supplementary examples in the publication by Marfurt, K. J., et al.: 3-D seismic attributes using a semblance-based coherency algorithm.—In: Geophysics, 1998, volume 63, page 1150–1165.
All previously mentioned, known methods perform the measurement of a similarity value in cells within a three-dimensional volume of seismic poststack data. The cells possess a fixed form and size in the spatial horizontal plane. The partial sequences of seismic traces that are contained in a cell, contribute with a horizontally constant weight to the derivation of individual similarity values for single pairs of traces, or of a general similarity value for the whole cell. Hence, the trace weighting jumps from a constant positive level inside the cell to the value zero outside the cell. This means, that all methods cannot the take into account the degree of spatial continuity of geological bodies, as it is derived e.g. by variographic analysis, since neighborhood relations are not weighted. Variography calculation and modeling is a prerequisite of geostatistics. It is used to describe quantitatively the distance dependent, and, if appropriate as well direction dependent spatial relations of neighboring points.